Invasive species are a cause for concern in natural and economic systems and require both monitoring and management. There is a trade-off between the amount of resources spent on surveying for the species and conducting early management of occupied sites, and the resources that are ultimately spent in delayed management at sites where the species was present but undetected. Previous work addressed this optimal resource allocation problem assuming that surveys continue despite detection until the initially planned survey effort is consumed. However, a more realistic scenario is often that surveys stop after detection (i.e., follow a “removal” sampling design) and then management begins. Such an approach will indicate a different optimal survey design and can be expected to be more efficient. We analyze this case and compare the expected efficiency of invasive species management programs under both survey methods. We also evaluate the impact of mis-specifying the type of sampling approach during the program design phase. We derive analytical expressions that optimize resource allocation between monitoring and management in surveillance programs when surveys stop after detection. We do this under a scenario of unconstrained resources and scenarios where survey budget is constrained. The efficiency of surveillance programs is greater if a “removal survey” design is used, with larger gains obtained when savings from early detection are high, occupancy is high, and survey costs are not much lower than early management costs at a site. Designing a surveillance program disregarding that surveys stop after detection can result in an efficiency loss. Our results help guide the design of future surveillance programs for invasive species. Addressing program design within a decision-theoretic framework can lead to a better use of available resources. We show how species prevalence, its detectability, and the benefits derived from early detection can be considered.